Matrix Factorization (Collaborative Filtering)

Description

Collaborative filtering is a technique used in recommendation systems. It analyzes relationships between users and interdependencies among products to identify new user-item associations.

A method of collaborative filtering uses matrix factorization. In its basic form, matrix factorization characterizes both items and users by vectors of factors inferred from item rating patterns.

Parameters

$n$: dimension of matrix

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
LU Matrix Decomposition	1945	$O(n^{3})$	$O(n^{2})$	Exact	Deterministic
QR Matrix Decomposition	1955	$O(n^{2})$	$O(n^{2})$	Exact	Deterministic
Cholesky Decomposition	1983	$O(n^{2})$	$O(n^{2})$	Exact	Deterministic

Time Complexity Graph

Space Complexity Graph

Time-Space Tradeoff